HotPaw Talking Tuner is a hands-off, sound-activated, talking musical instrument tuner. It uses speech synthesis to talk and tell you if a sound is in tune or not, so you don't have to look at your Mac. Talking Tuner does not require that VoiceOver be enabled.
A few years ago, I received a request to develop an iPhone app that could assist a vision-impaired individual with tuning their musical instruments. This is a Mac version of the iOS HotPaw Talking Tuner app.
Talking Tuner will listen for a note to be played, and then, after waiting for the end of the sound (so as not to talk over it), will speak the note name, and how many cents sharp or flat the end of the note is estimated to be.
Using headphones may help make it easier to hear what this app is saying while tuning. Make sure to turn the volume up high enough to hear it.
The pitch estimation algorithm works best for notes between 2 octaves below Middle-C to 2 octaves above Middle-C. It may not work as well for very low notes, very high notes, or with any background noise, harmony, or accompaniment present. The default tuning resolution is about +- 3 cents (3/100ths of the pitch difference between semitones). Optional higher resolution tuning settings available in the app's Preferences may result in a slower tuning response.